Banking is full of paradoxes. Governments and regulators around the world are on a drive to make banks safe, so that the current crisis can never happen again. The catchphrases are that assets should be "de-risked" and balance sheets "de-leveraged", while President Obama has openly applauded the "shrinking" of the financial sector. But nothing is more certain than that further shrinkage of bank balance sheets would intensify the most severe global downturn since the 1930s.

The paradox of excess banking regulation — that the removal of risk from bank balance sheets aggravates deflationary pressures — arises from an accounting identity. Come hell or high water, assets and liabilities must always be equal. In banking, this means the sum of cash, loans and securities the banks own must be equal to the capital, bonds and liabilities which banks owe to their shareholders and customers.

In most countries, roughly 90 per cent of banks' liabilities are to depositors. As far as depositors are concerned, their claims on the banks have an important advantage over other types of wealth. Bank deposits can be used to make payments. It follows that — to the extent that programmes of "de-risking" and "de-leveraging" reduce bank assets, to the extent that they eliminate "toxic assets" and lead to the calling-in of bad loans — they also lower banks' liabilities and destroy money. Thus, the greater the regulators' zeal in eliminating risk, the more rapid is the destruction of money balances.

Economics may be a controversial subject, but almost everyone accepts that the rapid destruction of money balances is madness. Ultimately, a good relationship holds between the quantity of money and nominal national income. In the medium term, the relationship may be less reliable, but a reasonable rule of thumb is that a sharp drop in money will lead to recession. In time spans of a few months, a big fall in bank deposits may not prompt much public comment, but in private it will cause companies and investors to notice a cash squeeze and to consider remedial budget cuts.

In America's Great Depression of the 1930s, the quantity of money tumbled by 40 per cent in four years. In today's Great Recession, a recurrent pattern across the top economies is that money growth has fallen and companies are strapped for cash. Fortunately, the money slowdown is generally less severe than it was in the horror of almost 80 years ago. For example, in the Eurozone, the M3 money measure has now been flat since last October, but it has not gone down.

Is it now too late to restrain the regulators? They undoubtedly see themselves as following the path of righteousness and have wide support in their attack on wicked bankers. When Dominic Strauss-Kahn, the managing director of the International Monetary Fund, proclaims that "speedy recovery" depends "on cleansing banks' balance sheets of toxic assets", he is listened to with respect. When he claims that "the primary objective must be to get the stalled machinery of the financial sector moving again", he can expect to be praised in the newspapers.

But — despite Strauss-Kahn's appeal to 122 country studies — he is incorrect. The message of all financial crises is that policy-makers' priority must be to stop the quantity of money falling and to get it rising again. That is what matters above all. If Strauss-Kahn intends by the "cleansing of bank balance sheets" that banks must shed assets and shrink their balance sheets, he is proposing to lower the quantity of money and aggravate the recession.

In the early 1930s, the US Treasury Secretary, Andrew Mellon, gave his advice on how to deal with the economy. "Liquidate labour, liquidate stocks, liquidate the farmers, liquidate real estate." The doctrine of liquidationism was exactly the wrong answer. If one person spent less, that was lower income for someone else. If one company repaid its bank loan rather than invested in new equipment, that was less money in the bank balance of the equipment supplier. The essence of liquidationism was the retreat to extreme safety, but its wider result was a deflationary disaster.

The pressure on banks to "de-risk" and to "de-leverage" is the modern version of liquidationism. Of course, banks must over time recognise their mistakes and take losses. But the right moment to announce losses is when the recovery is well established and banks are making good profits on new business. It would be a tragedy if the paradox of excess regulation — that the search for safety at the level of each particular bank can cut the money supply and aggravate demand weakness in the whole economy — leads to a continuation of the global recession in 2010.